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Markus K. Brunnermeier
1
Represent. Agent “Euler Equation Finance”
No (funding) friction Financial sector is a veil
Starting with Lucas …
Perfect aggregation
Pricing kernel = MRS of representative household
Modeling: exotic preferences/utility functions + beliefs
Data source: Consumption2
HH consumptiont
A-Pricest
Euler Equation
Note: no causality
“Institutional Finance”
Funding frictions are at the centerinvestors with expertise rely on funding w/o expertise
No aggregation
Market Failure
Pricing Kernel = Shadow cost of funding (liquidity)
Modeling: institutional frictions
Data source: Flow of funds 3
A-PricesHH
A
B
C
D
Flow of Funds
Financial Institutions
Funding and Market Liquidity (with Lasse Pedersen)
Funding Liquidity Ease … raise funds by
using asset as collateral m + x+ + m- x-≤ W Lagrange multiplier Margins/haircuts can
be changed every day Short-term lending 4
Uninformed
Households
Leveraged Experts
Financiers
•Margins•Haircuts•Collateral
HH HH
Asset prices
•Bid-ask spread•Market depth
Market Liquidity Ease with which one can
raise funds by selling asset
Asset price
pricing kernel
Liquidity spirals
Loss spiral
same leverage
mark-to-market
Margin/haircut spiral
delever!
mark-to-model
Reduced Positions
Higher Margins
Market LiquidityPrices Deviate
Funding LiquidityProblems
Losses on Existing Positions
Initial Lossese.g. credit
Brunnermeier-Pedersen (2009)
Margin/haircut spiral - Procyclicality
Margins/haircut increase in times of crisis delevermargin = f(risk measure)
Two Reasons
1. Backward-looking estimation of risk measure
Use forward looking measures
Use long enough data series
2. Adverse selection
Debt becomes more information sensitive (not so much out of the money anymore)
Credit bubbles
whose bursting undermines financial system
Countercyclical regulation
cashflow
Margin/haircut spiral - Procyclicality
Margins/haircut increase in times of crisis delevermargin = f(risk measure)
Two Reasons
1. Backward-looking estimation of risk measure
Use forward looking measures
Use long enough data series
2. Adverse selection
Debt becomes more information sensitive (not so much out of the money anymore)
Credit bubbles
whose bursting undermines financial system
Countercyclical regulation
cashflow
Fire-sale externality
Liquidity Spiral
Amplification
Fragility
Multiple EquilibriaSystemic risk is endogenous
Precuniary externality + incomplete markets
Take on too much leverage/maturity mismatch
take fire-sale price as given
also in Stiglitz (1982), Geanakoplos-Polemarchakis (1986)
81. Fire-sales depress price also for others
wealth of experts
Other Externalities/Financing Frictions
1. Hoarding
Micro-prudent SIV might draw on credit line
At the same time interbank market is closed
Macro-prudent?
2. Runs – dynamic co-opetition
3. Network Externality
Hiding own’s commitment uncertainty for counterparties
See JEP article
Overview
Institutional Finance Liquidity Spiral: Amplification, Fragility, Multiplicity
– with Lasse Pedersen
Procyclicality
Fire-sale Externality
Implications for Financial Regulation CoVaR – with Tobias Adrian
Implications for Monetary Economics – with Arvind Krishnamurthy
Role of financial institutions
Maturity Rat Race – with Martin Oehmke
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Current bank regulation
1. Risk of each bank in isolation Value at Risk
2. Focus on asset side of the balance sheet matter
Asset side Asset by asset – risk weighted diversify in off-balance SPV
Value at Risk (VaR)
Liability side – maturity mismatch gets little attention
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VaR
1%
Two challenges ….
1. Focus on externalities – systemic risk contribution What are the externalities? How to measure contribution to systemic risk?
CoVaR influences Who should be regulated? (AIG, …) What is the optimal capital charge (cap), Pigouvian tax Private insurance scheme?
2. Countercyclical regulation How to avoid procyclicality?
+ incorporate liquidity risk – asset-liability interaction
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1. Externality: Measure contribution of institution to systemic risk: CoVaR Response to current regulation
“hang on to others and take positions that drag others down when you are in trouble” (maximize bailout probability)
become big become interconnected
2. Procyclicality: Lean against “credit bubbles” – laddered response Bubble + maturity mismatch impair financial system (vs. NASDAQ bubble)
Impose Capital requirements/Pigouvian tax/Private insurance scheme not directly on ∆CoVaR, but on frequently observed factors, like maturity mismatch, leverage, B/M,
crowdedness of trades/credit, …
Macro-prudential regulation
Overview
Institutional Finance
Implications for Financial Regulation
contribution vs. exposure CoVaR
Quantile Regressions
Addressing Procyclicality
Market variables
Implications for Monetary Economics
Maturity Rat Race – with Martin Oehmke
15
CoVaR
CoVaR = VaR conditional on institute i (index) is in distress (at it’s VaR level)
Exposure CoVaR Q1: Which institutions are most exposed if there is a systemic crisis?
VaRi | system in distress
Contribution CoVaR
Q2: Which institutions contribute (in a non-causal sense)
VaRsystem| institution i in distress
Non-causal, can be driven by common factor
Cover both types Institutions
Risk spillovers “individually systemic”
Tail risk correlations “systemic as part of a herd”
Quantile Regressions: A Refresher
OLS Regression: min sum of squared residuals
Quantile Regression: min weighted absolute values
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2arg minOLS
t t ty x
if 0arg min
1 if 0
t t t tq
t
t t t t
q y x y x
q y x y x
20
-10
-50
5
-10 -5 0 5 10CS/Tremont Hedge Fund Index
Fixed Income Arbitrage 50%-Sensitivity
5%-Sensitivity 1%-Sensitivity
q-Sensitivities
Quantiles = -Value-at-Risk
Quantile regression:
Quantile q of y as a linear function of x
where F-1(q|x) is the inverse CDF conditional on x
Hence, F-1(q|x) = q% Value-at-Risk conditional on x.
Note out (non-traditional) sign convention!
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-1ˆ | |q y q qy x F q x x
CoVaR - using quantile regressions
Illustration: Same individual VaR, but A’s CoVaR > B’s CoVaR
Analogy to Covariance in CAPM
Various conditionings?1. Exposure CoVaR: Individual institution on financial index Who is vulnerable/exposed to?
2. Contribution CoVaR: Financial index on individual institution Who contributes?
3. Risk Spillover: Institution/strategy i on institution/strategy j
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CoV aRijq = V aRiqjV aRjq = ®̂ijq +^̄ijq V aR
jq
¢CoV aRijq = CoV aRijq ¡ V aRiq
i
q
ij
q
ij
q
j
q
ij
q
ij
q
j
q
i
q
ij
q
VaRCoVaRCoVaR
VaRVaRVaRCoVaR |
Data
(Commercial bank and security broker dealer industry portfolios from Ken French 1926/07-2008/12)
NYFed primary dealer (US) + GSE: CRSP returns 1986/01-2008/12 (weekly)[equity returns to also capture asset and liability]
Commercial banks
Investment banks
Portfolios sorted in quintiles based on Maturity mismatch, liquidity, size, B/M, cash/asset, equity vol.
CDS and option data of top 10 US banks, daily 2004-2008
CSFB/Tremont hedge fund strategies 1994/1-2008/12 (monthly) Long/Short Equity, Global Macro, Event Driven, Fixed Income Arbitrage,
Multi-Strategy, Emerging Markets, Equity Market Neutral, Convertible Arbitrage, Managed Futures, Dedicated Short Bias
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Overview
Institutional Finance
Implications for Financial Regulation
CoVaR contribution vs. exposure
Quantile Regressions
CoVaR versus VaR
Addressing Procyclicality
Market variables
Implications for Monetary Economics
Maturity Rat Race – with Martin Oehmke
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Q1: Who is in distress during systemic crisis?
VaR and ¢CoVaRexprelationship is very weak
Data up to 12/07
Most vulnerable Lehman Morgan Stanley Countrywide Bank of
America Bear Stearns
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-10
-8
-6
-4
-2
0
-21 -16 -11 -6
CoVaRiexp
VaRiPortfolios Commercial Banks
BSC
MER
LEH
MS
C
JPM
BAC
GS
JPM - old
C - old
CS
PWJ
CGM
BK
BTFRE
FNM
WB
WFC
Q2: Who “contributes” to systemic risk?
VaR does not capture systemic risk contribution ¢CoVaRcontri
Data up to 2007/12
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-5
-4
-3
-2
-1
0
-21 -16 -11 -6
CoVaRicontri
VaRiPortfolios Commercial Banks
Investment Banks GSE
BSCMER
LEH
MS
C
JPM
BAC
GS
JPM - old
C - old
CS
PWJ
BK
BT
CGM
WB
FNMFRE
WFC
Overview
Institutional Finance
Implications for Financial Regulation
contribution vs. exposure CoVaR
Quantile Regressions
Addressing Procyclicality Time-varying CoVaRs
Link to characteristics
Market variables
Implications for Monetary Economics
Maturity Rat Race – with Martin Oehmke
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Time-varying CoVaR
Relate to macro factors interpretation VIX Level “Volatility”
3 month yield
Repo – 3 month Treasury “Flight to Liquidity”
Moody’s BAA – 10 year Treasury “Credit indicator”
10Year – 3 month Treasury “Business Cycle”
(House prices)
(Aggregate Credit growth/spread)
(Haircut/margins (LTC ratios))… let’s figure out what matters!
Obtain Panel data of CoVaR
Next step: Relate to institution specific (panel) data
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Average factor exposure
INSTITUTIONS PORTFOLIOS
VaRindex VaRi CoVaRicontr CoVaRi
exp VaRi CoVaRicontr CoVaRi
exp
VIX -0.20 -0.28 -0.11 -0.15 -0.18 -0.14 -0.13
(-2.04) (-4.93) (-3.56) (-3.43) (-1.33) (-2.82) (-2.52)
3 Month Yield 0.31 -0.24 -0.20 -0.74 -0.09 0.05 -0.24
(1.41) (-0.97) (-3.93) (-2.36) (-0.53) (0.32) (-1.06)
Repo spread -4.56 -3.30 -2.61 0.08 -4.65 -1.39 0.91
(-1.80) (0.31) (-6.60) (-0.03) (-1.45) (-1.14) (0.46)
Credit spread -0.86 -1.09 -0.86 -2.63 -2.89 -0.83 -1.38
(-0.65) (0.90) (-3.61) (-4.23) (-1.91) (-1.55) (-2.12)
Term spread 0.15 -0.11 -0.21 -0.69 0.33 0.12 0.17
(0.40) (0.21) (-2.80) (-2.07) (0.33) (0.56) (0.44)
Average t-stats in parenthesis
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Avoid Procyclicality
Regulatory charges on ∆CoVaRcontri may introduce procyclicality Like VaR does in Basel II framework
Way out:Link + predict ∆CoVaRcontri to frequently observed characteristics (use Panel data structure)
Maturity mismatch
Leverage
…. special data only bank supervisors have (e.g. crowdedness)
Extra: Show that these variable carry information beyond VaR
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Predictive (1 year lag)
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PANEL A: INSTITUTIONS PANEL B: PORTFOLIOS
CoVaRicontri CoVaRi
exp CoVaRicontri CoVaRi
exp
(1) (2) (3) (4) (1) (2) (3) (4)
FE, TE FE FE, TE FE FE, TE FE FE, TE FE
VaR (lag) 0.02** 0.05*** -0.06** 0.03* 0.20*** 0.14*** -0.26***
Mat-Mism(lag) -0.30 -0.30 -1.84** -1.79** 1.20*** 0.25 0.04
Leverage (lag) -0.02*** -0.02*** -0.01 -0.02 -0.01*** -0.04*** -0.01*
B/M (lag) -0.27** -0.19** -0.08 0.71*** -0.14 0.57*** -0.53***
Size (lag) 9.94 10.61 27.43* -15.68 -0.52 -1.34 2.52
Constant -0.35 -0.65** -5.04*** -3.84*** -0.55** -0.63*** -6.13***
Observations 1657 1657 1657 1657 2486 2486 2486
R-squared 0.66 0.40 0.62 0.48 0.72 0.38 0.71
Predicting with Market Variables
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∆CoVaR_contrib ∆CoVaR_exp
COEFFICIENT 1 Quarter 1 Year 1 Quarter 1 Year 1 Quarter 1 Year 1 Quarter 1 Year
CDS_beta (lag) -0.25*** -0.58** -1.24*** -2.54***
(0.05) (0.23) (0.39) (0.85)
∆CDS (lag) 0.05 0.06 1.39 -1.28
(0.17) (0.68) (1.10) (2.20)
IV_beta (lag) -0.34*** -0.67*** -1.75*** -3.33**
(0.11) (0.18) (0.30) (1.39)
DIV (lag) -0.05 -0.77*** 0.63 -0.56
(0.28) (0.19) (0.59) (1.04)
Constant -1.17*** -1.28*** -1.13*** -1.15*** -4.65*** -4.82*** -4.33***-4.20***
(0.04) (0.07) (0.07) (0.08) (0.15) (0.24) (0.17) (0.52)
Observations 178 148 178 148 178 148 178 148
R-squared 0.59 0.54 0.55 0.55 0.71 0.68 0.72 0.65
1) beta w.r.t. first principal component on changes in CDS spreads within quarter2) panel regression with FE – (no findings with FE+TE)
Shock Amplifier vs. Absorber
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INSTITUTIONS
VaR_index VaR_index
COEFFICIENT 1 Year 1.5 Years 1 Year 1.5 Years
Fitted CoVaR_contrib (lag) 4.46** 6.43***
(1.91) (1.95)
Resid CoVaR_contrib (lag) 0.50 0.52
(0.40) (0.41)
Fitted CoVaR_exp (lag) 0.75 0.51
(1.42) (1.34)
Resid CoVaR_exp (lag) 2.94*** 3.95***
(0.57) (0.54)
VaR_index (lag) 0.30** 0.13 -1.25*** -1.96***
(0.12) (0.12) (0.33) (0.32)
Overview
Institutional Finance
Implications for Financial Regulation – CoVaR Macro-prudential regulation Focus on externalities
Measure for systemic risk is needed, e.g. CoVaR
Maturity mismatch (+ Leverage) – encourage long-term funding
Countercyclical regulation Find variables that predict average future CoVaR
Forward-looking measures, spreads, …
Implications for Monetary Economics Role of financial institutions
Maturity Rat Race
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Implications for Monetary Economics
Monetary Transmission Target rate (short-term) Effective rate (short-term) Corporate lending rate
Liquidity policy Narrow: Hold short-term rate close to target
Reduce term risk premium Broad: financial stability to ensure transmission
Reduce term and credit risk premium
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Objectives Instruments
Price stability Target rate (money supply)
Financial stability Liquidity policyTinbergen
maturity
credit risk
target
Need to understand the role of financial institutions first
Role of Financial Institutions
Project/asset selection Informational advantage (Sharpe, Rajan)
Create info-insensitive securities (Gorton-Pennachi)
Pool and tranch in order to reduces lemon’s problem
Maturity transformationWhy short-term (debt) funding? Liquidity shock insurance (Diamond-Dybvig)
maturity tranformation is good, but bank run caveat
Incentivize management (Calomiris-Kahn) Maturity mismatch is good
Maturity rat race (with MartinOehmke) Maturity mismatch is bad
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The Maturity Rat Race
Leads to a unraveling to short-term debt
Friction with multiple creditors with differing maturities
Mechanism:
Creditors with shorter maturity can adjust face value (reduce interest rate) since they can pull out in bad states
Part of cost in low state is borne not by borrower but by remaining long-term creditors (long-term debt holders are diluted)
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Setup
Financing can be
Long-term: two periods
Short-term: one period + rollover at t=1
Borrower has to borrow from multiple lenders
Continuum of competitive lenders
Each has limited capital
Priority in default
Proportional to face value of debt at time of default
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Project Payoffs
Long-term project costs 1 at t=0, pays out at t=2 Expected payoff moves along binominal tree, u=1/d
Project can be liquidated prematurely at discount: fraction (1-δ) is lost
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The Maturity Rat Race
Hold everybody else’s financing fixed, can borrower and one lender profitably deviate by moving to rollover financing?
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When is the Rat Race Inefficient?
1. Inefficient (early) unwinding in down state
2. Project does not get off the ground (since long-term financing is not viable)
When economy turns sour/riskyproblem becomes more severe
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1)1( dXuX
uXdX 1
Inefficiencies
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Covenants limit Rat Race
Since
E.g. covenant restrict raising face value of new short-term debt at time t=1
Short-term debt holders always pull out in down state
Short-term financing trap (multiplicity)
If all lenders go short-term + pull out in down state at t=1, then borrower does not want to switch to “expensive” long-term financing
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Covenants – Short-term Financing Trap
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Conclusion
Institutional Finance Financial institutions are not a veil
Moving away from representative agent models
Financial Regulation Macro-prudential has to focus on measuring
contribution to systemic risk
Countercyclicality (to overcome margin/haircut spiral)
Monetary/Liquidity Policy Role of financial institutions – why short-term funding?
Avoid “credit bubbles” since they impair financial system
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